\(\frac{w}{3}-\frac{w}{8}=-\frac{1}{24}\)

To solve the equation \(\frac{w}{3} - \frac{w}{8} = -\frac{1}{24}\), we'll follow these steps:

### Step 1: Find a common denominator for the fractions on the left side.
The denominators are 3 and 8. The least common denominator (LCD) of 3 and 8 is 24. 

### Step 2: Rewrite each fraction with the common denominator.
\[
\frac{w}{3} = \frac{8w}{24}, \quad \frac{w}{8} = \frac{3w}{24}
\]
Now, substitute these into the equation:
\[
\frac{8w}{24} - \frac{3w}{24} = -\frac{1}{24}
\]

### Step 3: Combine the fractions on the left side.
Since the denominators are the same, combine the numerators:
\[
\frac{8w - 3w}{24} = -\frac{1}{24}
\]
This simplifies to:
\[
\frac{5w}{24} = -\frac{1}{24}
\]

### Step 4: Solve for \(w\).
To eliminate the fraction, multiply both sides of the equation by 24:
\[
5w = -1
\]
Now, divide both sides by 5:
\[
w = -\frac{1}{5}
\]

### Final Answer:
\[
w = -\frac{1}{5}
\]

Would you like any details or have any questions?

Here are five related questions to explore further:

1. How do you solve similar equations involving fractions with different denominators?
2. What are some strategies to find the least common denominator (LCD)?
3. How do you check your solution to an equation?
4. What is the impact of multiplying both sides of an equation by the same number?
5. How do you solve equations where fractions have variables in the denominator?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation w/3 - w/8 = -1/24 with a detailed step-by-step solution. This problem involves solving equations with fractions and is suitable for students in Grades 7-9.

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